A lifeguard is in an observation chair and spots a person who needs help. The angle of depression to the person is 22°. The eye level of the lifeguard is 10 feet above the ground. What is the horizontal distance between the lifeguard and the person? Round to the nearest foot.

The horizontal distance between the lifeguard and the person is approximately 24.751 feet.

Step-by-step explanation:

At first we include a geometrical representation of the statement, which is shown in the image attached below. We can determine the horizontal distance between the lifeguard and the person by means of the following trigonometrical relationship:

(1)

Where:

- Angle of depression to the person, measured in sexagesimal degrees.

- Height of the lifeguard above the ground, measured in feet.

- Horizontal distance between the lifeguard and the person, measured in feet.

If we know that and , then the horizontal distance between the lifeguard and the person is:

The horizontal distance between the lifeguard and the person is approximately 24.751 feet.

that is the sum

step-by-step explanation:

there are no other answers without knowing the variables values

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places